A direct, constructive proof is given for the basic representation theorem for convex domination of measures. The proof is given in the finitistic case Žpurely . atomic measures with a finite number of atoms , and a simple argument is then given to extend this result to the general case, including both probability measures and finite Borel measures on infinite-dimensional spaces. The infinite-d...

where H is the Hamiltonian (”energy”) and {. , .} is a Poisson bracket on an infinite dimensional phase space, called Poisson manifold. Unlike finite dimensional Hamiltonian systems, which are ordinary differential evolution equations on finite dimensional phase spaces, for which general existence and uniqueness theorems for solutions exist, this is not the case for PDEs. There are no general e...